Consider a cyclist pedaling a bicycle. When a force is exerted on the pedal, the crankshaft rotates such that the chain attached to the crankshaft exerts a force on the cogs of the wheel. On establishing a coordinate system, the tangential force on the cogs is along the x-axis, while the radius of the cogs is the moment arm expressed in terms of the position vector. Here, the moment of force about point O is along the y-direction perpendicular to both the force and position vector and is expressed as the cross product of the position and force vectors. The cross-product can be solved by expressing the coefficient of components of force and position vector in the form of a determinant. Expanding the determinant, the moment's component along the x-axis is expressed in terms of the y and z components of the force and position vector. Similarly, expressing its other two components in terms of force and position vector components, the moment of a force can be expressed in cartesian vector form.